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151
thesis/chapters/chap5_alcap_setup.tex
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@@ -402,10 +402,11 @@ correlation between detectors would be established in the analysis stage.
At the beginning of each block, the time counter in each digitiser is reset to At the beginning of each block, the time counter in each digitiser is reset to
ensure time alignment across all modules. The period of 110~ms was chosen to be: ensure time alignment across all modules. The period of 110~ms was chosen to be:
{\em i} long enough compares to the time scale of several \si{\micro\second}\ of the {\em i} long enough compared to the time scale of several \si{\micro\second}\
physics of interest, {\em ii} short enough so that there is no timer rollover of the physics of interest, {\em ii} short enough so that there is no timer
on any digitiser (a FADC runs at its maximum speed of \SI{170}{\mega\hertz} could rollover on any digitiser (a FADC runs at its maximum speed of
handle up to about \SI{1.5}{\second} with its 28-bit time counter). \SI{170}{\mega\hertz} could handle up to about \SI{1.5}{\second} with its
28-bit time counter).
To ease the task of handling data, the data collecting period was divided into To ease the task of handling data, the data collecting period was divided into
short runs, each run stopped when the logger had recorded 2 GB of data. short runs, each run stopped when the logger had recorded 2 GB of data.
@@ -495,8 +496,8 @@ the recorded pulse height spectrum is shown in \cref{fig:ge_eu152_spec}. The
source was placed at the target position so that the absolute efficiencies can source was placed at the target position so that the absolute efficiencies can
be calculated. The peak centroids and areas were obtained by fitting a Gaussian be calculated. The peak centroids and areas were obtained by fitting a Gaussian
peak on top of a first-order polynomial background. The only exception is the peak on top of a first-order polynomial background. The only exception is the
\SI{1085.84}{\keV} line because of the interference of \SI{1089.74}{\keV}, \SI{1085.84}{\keV} line because of the interference of the \SI{1089.74}{\keV}
the two were fitted with two Gaussian peaks on top of a first-order gamma, the two were fitted with two Gaussian peaks on top of a first-order
polynomial background. polynomial background.
The relation between pulse height in ADC value and energy is found to be: The relation between pulse height in ADC value and energy is found to be:
@@ -527,30 +528,86 @@ a little worse at 3.1~\si{\keV}~for the annihilation photons at
\label{fig:ge_fwhm} \label{fig:ge_fwhm}
\end{figure} \end{figure}
The absolute efficiencies of the referenced points, and calculated Following corrections for the peak areas are considered:
efficiencies at the X-ray of interest are presented in
\cref{tab:xray_eff}.
%The absolute efficiencies for the $(2p-1s)$ lines of aluminium
%(\SI{346.828}{\keV}) and silicon (\SI{400.177}{\keV})
%are presented in \cref{tab:xray_eff}.
In the process of efficiency calibration,
corrections for true coincidence summing and self-absorption were not applied.
The true coincidence summing probability is estimated to be very
small, about \num{5.4d-6}, thanks to the far geometry of the calibration. The
absorption in the source cover made of \SI{22}{\mg\per\cm^2}
polyethylene is less than \num{4d-4} for a \SI{100}{\keV} photon.
A Monte Carlo (MC) study on the acceptance of the germanium detector with two
purposes:
\begin{enumerate} \begin{enumerate}
\item compare between measured and MC efficiencies: a point source made of \item Correction for counting loss due to finite response time of the
$^152$Eu is placed at the target position detector system, where two gamma rays arrive at the detector within a time
\item estimate the uncertainty due to finite-size geometry: the source is interval short compared to that response time. This correction is
made of silicon with the same dimensions as those of the thick silicon significant in our germanium system because of the current pulse
detector, namely \SI[product-units=power]{1.5 x 50 x 50}{\mm}; then the information extracting method does not count the second pulse.
primary vertex of $^152$Eu is generated inside the source. \item Correction of counting time loss in the reset periods of the transistor
reset preamplifier. A preamplifier of this type would reset itself after
accumulating a predetermined amount of charge. During a reset, the
preamplifier is insensitive so this can be counted as dead time.
\item True coincidence summing correction: two cascade gamma rays hit the
detector at the same time would cause loss of count under the two
respective peaks and gain under the sum energy peak.
\item Correction for self-absorption of a gamma ray by the source itself.
\end{enumerate} \end{enumerate}
The corrections for the first two mechanisms can be estimated by examining
pulse length and intervals between two consecutive pulses in the germanium
detector (\cref{fig:ge_cal_rate_pulselength}). The average pulse
length is \SI{45.7}{\um}, the average count rate obtained from the decay rate
of the interval spectrum is \SI{240}{\per\s}.
The correction factor for the finite response time of the detector system is
calculated as:
\begin{align}
k_{\textrm{finite response time}} &= e^{2\times \textrm{(pulse length)}
\times \textrm{(count rate)}}\\
&= e^{2\times 47.5\times10^{-6} \times 241} \nonumber\\
&= 1.02 \label{eqn:finite_time_response}
\end{align}
The resets of the preamplifier show up as a peak around \SI{2}{\ms},
consistent with specification of the manufacturer. Fitting the peak on top of
an exponential background gives the actual reset pulse length of
\SI{1947.34}{\us} and the number of resets during the calibration runs is
2335.0. The total time loss for resetting is hence:
$1947.34\times 10^{-6} \times 2335.0 = 4.55$ \si{\s}. That is a 0.14\% loss
for a measuring time of \SI{3245.5}{\s}. This percentage loss is insignificant
compared with the loss in \eqref{eqn:finite_time_response} and the statistical
uncertainty of peak areas so correction for amplifier resets is not applied.
\begin{figure}[htb]
\centering
\includegraphics[width=0.95\textwidth]{figs/ge_cal_rate_pulselength}
\caption{Germanium detector pulse length (left) and intervals between pulses
on that detector (right). The peak around \SI{2}{\ms} corresponds to the
resets of the preamplifier. The peak at \SI{250}{\us} is due to triggering
by the timing channel which is on the same digitiser.}
\label{fig:ge_cal_rate_pulselength}
\end{figure}
The true coincidence summing probability is estimated to be very small, about
\num{5.4d-6}, thanks to the far geometry of the calibration. The absorption in
the source cover made of \SI{22}{\mg\per\cm^2} polyethylene is less than
\num{4d-4} for a \SI{100}{\keV} photon. Therefore these two corrections are
omitted.
The absolute efficiencies of the reference gamma rays show agreement with those
obtained from a Monte Carlo (MC) study where a point source made of $^{152}$Eu
is placed at the target position (see \cref{fig:ge_eff_cal}). A comparison
between efficiencies in case of the point-like source and a finite-size
source is also done by MC simulation. As shown in \cref{fig:ge_eff_cal}, the
differences are in line with the uncertainties of the measured efficiencies.
%The dimensions of the latter are set to
%resemble the distribution of muons inside the target: Gaussian spreading
%\SI{11}{\mm} vertically, \SI{13}{\mm} horizontally, and \SI{127}{\um} in
\begin{figure}[htb]
\centering
\includegraphics[width=0.40\textwidth]{figs/ge_eff_cal}
\includegraphics[width=0.40\textwidth]{figs/ge_eff_mc_finitesize_vs_pointlike_root}
\caption{Absolute efficiency of the germanium detector, the fit was done with
7 energy points from 244~keV, the shaded area is
95\% confidence interval of the fit.}
%because it is known that the linearity between
%$ln(\textrm{E})$ and $ln(\textrm{eff})$ holds better.
\label{fig:ge_eff_cal}
\end{figure}
The absolute efficiencies of the referenced points, and calculated efficiencies
at X-rays of interest are listed in \cref{tab:xray_eff}.
\begin{table}[htb] \begin{table}[htb]
\begin{center} \begin{center}
\pgfplotstabletypeset[ \pgfplotstabletypeset[
@@ -601,18 +658,6 @@ purposes:
\label{tab:xray_eff} \label{tab:xray_eff}
\end{table} \end{table}
\begin{figure}[htb]
\centering
\includegraphics[width=0.40\textwidth]{figs/ge_eff_cal}
\includegraphics[width=0.40\textwidth]{figs/ge_eff_mc_finitesize_vs_pointlike_root}
\caption{Absolute efficiency of the germanium detector, the fit was done with
7 energy points from 244~keV, the shaded area is
95\% confidence interval of the fit.}
%because it is known that the linearity between
%$ln(\textrm{E})$ and $ln(\textrm{eff})$ holds better.
\label{fig:ge_eff_cal}
\end{figure}
% subsection germanium_detector (end) % subsection germanium_detector (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection{Beam tuning and muon momentum scanning} %\subsection{Beam tuning and muon momentum scanning}
@@ -684,12 +729,12 @@ different targets were carried out for silicon targets:
As the emitted protons deposit a significant amount of energy in the target As the emitted protons deposit a significant amount of energy in the target
material, thin targets and thus excellent momentum resolution of the low energy material, thin targets and thus excellent momentum resolution of the low energy
muon beam are critical. Aluminium targets of 50-\si{\micro\meter}\ and muon beam are critical, aluminium targets of 50-\si{\micro\meter}\ and
100~\si{\micro\meter}\ thick were used. Although a beam with low momentum spread of 100-\si{\micro\meter}\ thick were used. Although a beam with low momentum
1\% is preferable, it was used for only a small portion of the run due to the spread of 1\% is preferable, it was used for only a small portion of the run
low beam rate (see \cref{fig:Rates}). The beam momentum for each target due to the low beam rate (see \cref{fig:Rates}). The beam momentum for each
was chosen to maximise the number of stopped muons. The collected data sets are target was chosen to maximise the number of stopped muons. The collected data
shown in \cref{tb:stat}. sets are shown in \cref{tb:stat}.
\begin{table}[btp!] \begin{table}[btp!]
\begin{center} \begin{center}
@@ -865,20 +910,8 @@ update the plots to reflect real-time status of the detector system.
Some offline analysis modules has been developed during the beam time and could Some offline analysis modules has been developed during the beam time and could
provide quick feedback in confirming and guiding the decisions at the time. For provide quick feedback in confirming and guiding the decisions at the time. For
example, the X-ray spectrum analysis was done to confirm that we could observe example, the X-ray spectrum analysis was done to confirm that we could observe
the muon capture process (\cref{fig:muX}), and to help in choosing optimal the muon capture process and to help in choosing optimal momenta which
momenta which maximised the number of stopped muons. maximised the number of stopped muons.
\begin{figure}[btp]
\centering
\includegraphics[width=0.7\textwidth]{figs/muX.png}
\caption{Germanium
detector spectra in the range of 300 - 450 keV with different setups: no
target, 62-\si{\micro\meter}-thick silicon target, and
100-\si{\micro\meter}-thick aluminium target. The ($2p-1s$) lines from
aluminium (346.828 keV) and silicon (400.177 keV) are clearly visible,
the double peaks at 431 and 438 keV are from the lead shield, the peak at
351~keV is a background gamma ray from $^{211}$Bi.}
\label{fig:muX}
\end{figure}
Although the offline analyser is still not fully developed yet, several modules Although the offline analyser is still not fully developed yet, several modules
are ready. They are described in detailed in the next chapter. are ready. They are described in detailed in the next chapter.

6
thesis/chapters/chap6_analysis.tex
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@@ -59,7 +59,7 @@ pulses on all detector channels, and picks all pulses occur in
a time window of \SI{\pm 10}{\si{\us}} around each candidate to build a time window of \SI{\pm 10}{\si{\us}} around each candidate to build
a muon event. A muon candidates is a hit on the upstream plastic scintillator a muon event. A muon candidates is a hit on the upstream plastic scintillator
with an amplitude higher than a threshold which was chosen to reject MIPs. The with an amplitude higher than a threshold which was chosen to reject MIPs. The
period of \SI{10}{\si{\us}} is long enough compares to the mean life time of period of \SI{10}{\si{\us}} is long enough compared to the mean life time of
muons in the target materials muons in the target materials
(\SI{0.758}{\si{\us}} for silicon, and \SI{0.864}{\si{\us}} (\SI{0.758}{\si{\us}} for silicon, and \SI{0.864}{\si{\us}}
for aluminium~\cite{SuzukiMeasday.etal.1987}) so practically all of emitted for aluminium~\cite{SuzukiMeasday.etal.1987}) so practically all of emitted
@@ -388,7 +388,7 @@ This number of X-rays needs to be corrected for following effects:
&= 1.06 &= 1.06
\end{align} \end{align}
The 2-ms-long reset pulses effectively reduce the actual measurement time The 2-ms-long reset pulses effectively reduce the actual measurement time
compares to other channels, so the correction factor for the effect is: compared to other channels, so the correction factor for the effect is:
\begin{align} \begin{align}
k_{\textrm{reset pulse}} &= \frac{\textrm{(measurement time)}} k_{\textrm{reset pulse}} &= \frac{\textrm{(measurement time)}}
{\textrm{(measurement time)} {\textrm{(measurement time)}
@@ -830,7 +830,7 @@ The uncertainty of the emission rate could come from several sources:
collimator. In the worst case when the muon beam is flatly distributed, collimator. In the worst case when the muon beam is flatly distributed,
that displacement could change the acceptance of the silicon detectors by that displacement could change the acceptance of the silicon detectors by
12\%. Although no measurement was done to determine the efficiency of the 12\%. Although no measurement was done to determine the efficiency of the
silicon detectors, it would have small effect compare to other factors. silicon detectors, it would have small effect compared to other factors.
\end{enumerate} \end{enumerate}
The combined uncertainty from known sources above therefore could be as large The combined uncertainty from known sources above therefore could be as large

24
thesis/thesis.bib
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@@ -462,6 +462,23 @@
Timestamp = {2014-04-08} Timestamp = {2014-04-08}
} }
@Article{Bichsel.2006,
Title = {A method to improve tracking and particle identification in TPCs and silicon detectors},
Author = {Bichsel, Hans},
Journal = {Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment},
Year = {2006},
Number = {1},
Pages = {154--197},
Volume = {562},
__markedentry = {[NT:6]},
Doi = {10.1016/j.nima.2006.03.009},
File = {Published version:Bichsel.2006.pdf:PDF},
Owner = {NT},
Publisher = {Elsevier},
Timestamp = {2014-09-16}
}
@Article{Bichsel.1988, @Article{Bichsel.1988,
Title = {{Straggling in Thin Silicon Detectors}}, Title = {{Straggling in Thin Silicon Detectors}},
Author = {Bichsel, H.}, Author = {Bichsel, H.},
@@ -1048,8 +1065,6 @@
Month = {Aug}, Month = {Aug},
Pages = {741--757}, Pages = {741--757},
Volume = {36}, Volume = {36},
__markedentry = {[NT:]},
Doi = {10.1103/PhysRevC.36.741}, Doi = {10.1103/PhysRevC.36.741},
File = {Published version:GadioliGadioli.1987.pdf:PDF}, File = {Published version:GadioliGadioli.1987.pdf:PDF},
Issue = {2}, Issue = {2},
@@ -1812,6 +1827,7 @@
Month = {Mar}, Month = {Mar},
Pages = {1106--1110}, Pages = {1106--1110},
Volume = {43}, Volume = {43},
Doi = {10.1103/PhysRevC.43.1106}, Doi = {10.1103/PhysRevC.43.1106},
File = {Published version:MartoffCummings.etal.1991.pdf:PDF}, File = {Published version:MartoffCummings.etal.1991.pdf:PDF},
Issue = {3}, Issue = {3},
@@ -2283,8 +2299,6 @@
Month = {Jan}, Month = {Jan},
Pages = {135--141}, Pages = {135--141},
Volume = {19}, Volume = {19},
__markedentry = {[NT:]},
Doi = {10.1103/PhysRevC.19.135}, Doi = {10.1103/PhysRevC.19.135},
File = {Published version:SchlepuetzComiso.etal.1979.pdf:PDF}, File = {Published version:SchlepuetzComiso.etal.1979.pdf:PDF},
Issue = {1}, Issue = {1},
@@ -2471,7 +2485,7 @@
Pages = {MOLT007}, Pages = {MOLT007},
Volume = {C0303241}, Volume = {C0303241},
__markedentry = {[NT:6]}, __markedentry = {[NT:]},
Archiveprefix = {arXiv}, Archiveprefix = {arXiv},
Eprint = {physics/0306116}, Eprint = {physics/0306116},
File = {arXiv v1:VerkerkeKirkby.2003-eprintv1.pdf:PDF}, File = {arXiv v1:VerkerkeKirkby.2003-eprintv1.pdf:PDF},

4
thesis/thesis.tex
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@@ -33,8 +33,8 @@ for the COMET experiment}
%\input{chapters/chap2_mu_e_conv} %\input{chapters/chap2_mu_e_conv}
%\input{chapters/chap3_comet} %\input{chapters/chap3_comet}
%\input{chapters/chap4_alcap_phys} %\input{chapters/chap4_alcap_phys}
\input{chapters/chap5_alcap_setup} %\input{chapters/chap5_alcap_setup}
%\input{chapters/chap6_analysis} \input{chapters/chap6_analysis}
%\input{chapters/chap7_results} %\input{chapters/chap7_results}
\begin{backmatter} \begin{backmatter}